For those of us who favor single-action semi-automatics—like the 1911 or the Browning Hi Power—one of the most important techniques to come out of the whole "Modern Technique of the Pistol" concept was the importance of riding the thumb safety. That is, once your shooting thumb has depressed the thumb safety it stays on the safety during the entire shooting sequence. There are two very good reasons for this.
The first reason is that it avoids unintentionally re-engaging the safety. As the pistol recoils, the shooting grip may become loose and cause the hand to move about on the pistol grip. This can cause the knuckle of the thumb to hit the bottom the the thumb safety, pushing it upwards. This, of course, would cause the safety to lock the slide and the pistol will not fire until the safety is disengaged. This will cost you points in a pistol match and it will cost your a lot more than that in the middle of a gunfight.
The second reason is that, with your thumb riding the thumb safety, you will just naturally take a higher grip on the pistol. The high grip places your hand closer to the axis of the bore. This, along with a good isometric two-handed grip on the pistol, will significantly reduce muzzle flip. All of which allows the shooter to deliver accurate follow-up shots more quickly.
There was a time when Col. Jeff Cooper and the gunsmiths at Gunsite even toyed with the idea of making the thumb safety spring loaded so that it would bounce back in the upward position if not depressed. The idea being that, if you weren't riding that safety the gun wouldn't work. Though they actually built some spring-loaded thumb safeties, it was decided that the best way to deal with the issue was through proper teaching and practice.
However, there are some shooters who cannot properly engage the grip safety when they are shooting in this manner. I am one of those. Using a beavertail grip safety with the lower end of the grip safety built up works for some shooters. Others may need to visit a competent pistolsmith and have the grip safety adjusted.
Every handgun style has its own little quirks and peculiarities that the shooter must learn if he expects to be effective with that design. If you like the 1911 pistol, try this technique for more effective pistol management and quick, accurate repeat shots.